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We developed equations to predict the asymptotic response due to two-stage selection, where first-stage selection was performed by using GEBVs based solely on genotypes and second-stage selection was performed with GEBVs that combined genotypes and phenotypes. The situation that we considered involved four-path selection executed as sires to breed sons, sires to breed daughters, dams to breed sons, and dams to breed daughters. We established two procedures to predict the response. The first incorporated correlated indices during the first and second-stage selections of two-stage selection. The other procedure used independent indices during two-stage selection. The response per generation in the initial generation was greater for the correlated indices than for the independent indices. However, the asymptotic response per generation was slightly greater for the independent indices than for the correlated indices. The asymptotic response per generation was lower during two-stage selection than during single-stage selection. However, the asymptotic response per year was greater for two-stage selection than for single-stage selection. In addition, that trend was more conspicuous when the economic weight was 1:3 for the first (h2 =0.3) to second (h2 =0.05) index trait compared with economic weights of 1:1 and 3:1. However, the magnitude of the response to the aggregate genotype-relative not to single-stage selection but to absolute magnitude was greater at an economic weight of 3:1 than at those of 1:1 and 1:3. The reduction in genetic variance from the initial to an asymptotic generation was greater for a scenario where young parents selected at the first-stage accounted for 30% of all parents in two-stage selection than where they accounted for 70%. The reduction in genetic variance of the aggregate genotype over generations was smaller for independent indices than correlated indices during two-stage selection. Our new formula for predicting genetic response applies to any combination of accuracies of GEBVs and intensities of selection. Therefore, the formula presented is a general equation for predicting genetic response over generations due to two-stage genomic index selection.

Asymptotic Genetic Response Due to Two-Stage Genomic Index Selection Derived from Correlated or Independent Indices during Both Stages